What jobs cannot be automatized by AI in the future?
The Oxford study from 2013 in The future of employment paper assess this and estimated the probability of computerisation for 702 detailed occupations using a Gaussian process classifier (using job data from the UK partially merged with data from US), and based on these estimates they identified three areas of computerisation bottleneck areas and nine skills that people are still needed for each profession, this includes:


Perception and Manipulation.


Finger dexterity.


  The ability to make precisely coordinated movements of
  the fingers of one or both hands to grasp, manipulate, or
  assemble very small objects.

Manual dexterity.


  The ability to quickly move your hand, your hand together
  with your arm, or your two hands to grasp, manipulate, or
  assemble objects.

The need for a cramped work space.


  How often does this job require working in cramped work
  spaces that requires getting into awkward positions?


Creative Intelligence.


Originality.


  The ability to come up with unusual or clever ideas about
  a given topic or situation, or to develop creative ways to
  solve a problem.

Fine arts.


  Knowledge of theory and techniques required to compose,
  produce, and perform works of music, dance, visual arts,
  drama, and sculpture.


Social Intelligence.


Social perceptiveness.


  Being aware of others’ reactions and understanding why
  they react as they do.

Negotiation.


  Bringing others together and trying to reconcile
  differences.

Persuasion.


  Persuading others to change their minds or behavior.

Assisting and caring for others.


  Providing personal assistance, medical attention, emotional
  support, or other personal care to others such as
  coworkers, customers, or patients.




Source: The future of employment: how susceptible are jobs to computerisation: Table 1.

What this study is basically saying, around 50% of all jobs will be replaced by robots in the next 20 years.

Based on the above study, the BBC assembled a handy guide that calculates which jobs are likely to be automated within the next two decades:


Will a robot take your job?


See also: replacedbyrobot.info website.


  With this tool, you can check the prediction of over 700 jobs.


Related:


When robots can do all manual labor and service jobs, what will the majority human population do?
TED: The jobs we'll lose to machines — and the ones we won't (by Anthony Goldbloom)
Labore Ad Infinitum: AI &amp; Automation vs Timeless Tasks

Which suggests: Military/Peacekeeper, Athletes, Therapist, Musical Performer, Actors and Dancer, Visual Artists, Religious/Spiritual Leaders, The World’s Oldest Profession, Virtual Goods, Politicians, Judges, Parenting.